Question: Solve for $x$ and $y$ using substitution. ${-3x-4y = -2}$ ${y = -2x-7}$
Solution: Since $y$ has already been solved for, substitute $-2x-7$ for $y$ in the first equation. ${-3x - 4}{(-2x-7)}{= -2}$ Simplify and solve for $x$ $-3x+8x + 28 = -2$ $5x+28 = -2$ $5x+28{-28} = -2{-28}$ $5x = -30$ $\dfrac{5x}{{5}} = \dfrac{-30}{{5}}$ ${x = -6}$ Now that you know ${x = -6}$ , plug it back into $\thinspace {y = -2x-7}\thinspace$ to find $y$ ${y = -2}{(-6)}{ - 7}$ $y = 12 - 7$ $y = 5$ You can also plug ${x = -6}$ into $\thinspace {-3x-4y = -2}\thinspace$ and get the same answer for $y$ : ${-3}{(-6)}{ - 4y = -2}$ ${y = 5}$